Altering a trigonometric function by multiplying it by a constant changes its graph by stretching it taller or squishing it flatter. This is called a change in amplitude. Altering it by multiplying its angle by a constant changes its graph by stretching / squishing it like a spring. This is called a change in period. In this lesson we learn the effect of these changes on the six trig functions.

Objectives

By the end of this topic you should know and be prepared to be tested on:

4.2.1 Given a trig function or graph of a trig function find its amplitude including knowing that amplitude is always positive

4.2.2 Know that a negative coefficient of a trig function means a reflection in the x-axis (i.e., flips the curve upside down)

4.2.3 Given a trig function or graph of a trig function find its period including using the formula (period of basic trig fn)/B

Terminology

Define: amplitude, period (of a trig function), periodic

Text Notes

You may SKIP any "curve fitting" and "regression" examples/problems in this section and throughout the course including "sine regression".

Supplementary Resources (recommended)

Explore how changing the "a" (amplitude) and "b" (period) values on the slider bar affect the sine graph at Sine Amplitude and Period from Desmos.